MYOFS

[STxAxTIC]

This is a bite-size piece of code that's been lingering on my desktop for a while and it needs a new home.

MYOFS stands for "Make your own Fibonacci sequence". It turns out that that usual 1 1 2 3 5 8 13... thing can be generalized. A little backstory first. The Fibonacci sequence, as we all know it, can actually be generated by doing something cute with the golden ratio. That is, a number close to 1.618 seeds the entire sequence. This program lets you change the seed parameter from the golden ratio to whatever you want, generating the appropriate sequence.

Once that gets boring, the game becomes finding new sequences that are all integers, not just a bunch of decimals. Welp, turns out there are many of these cases. Un-comment some other initial x-values to get them:

Code: QB64: [Select]

1. OPTION _EXPLICIT
2.  
3. DIM x AS DOUBLE
4. DIM Coefficient(21) AS DOUBLE
5. DIM k AS LONG
6. x = 1 / 2 + SQR(5) / 2
7. 'x = 1 + SQR(2)
8. 'x = 3 / 2 + SQR(13) / 2
9. 'x = 2 + SQR(5)
10. DO
11.     CLS
12.     IF (_KEYDOWN(18432) = -1) THEN ' Up-arrow
13.         x = x + .01
14.     END IF
15.     IF (_KEYDOWN(20480) = -1) THEN ' Down-arrow
16.         x = x - .01
17.     END IF
18.     _KEYCLEAR
19.     Coefficient(1) = 1
20.     Coefficient(2) = x - 1 / x
21.     PRINT "x="; x
22.     PRINT "C_1="; Coefficient(1)
23.     PRINT "C_2="; Coefficient(2)
24.     FOR k = 3 TO UBOUND(Coefficient)
25.         Coefficient(k) = -1 * Coefficient(k - 2) + x ^ (k - 1) + (-1) ^ (k - 1) * 1 / (x ^ (k - 1))
26.         PRINT "C_"; LTRIM$(RTRIM$(STR$(k))); "="; Coefficient(k) ', Coefficient(k) / Coefficient(k - 1)
27.     NEXT
28.     _LIMIT 60
29.     _DISPLAY
30. LOOP
31.  

[bplus]

I suspect Pythagorean Triples are in play for all integer sequences, I will check this out after I figure out how to defeat a certain pattern of moves against AI, ha, ha!

@STxAxTIC what's your favorite charity?